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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Integration is differentiable
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by Allan Gottlieb PDF
Proc. Amer. Math. Soc. 53 (1975), 167-171 Request permission

Abstract:

The integration map taking vector fields to flows is well known to be continuous. In this paper an elementary proof is given that the map is actually smooth if the domain and range are given appropriate topologies.
References
  • Ralph Abraham and Joel Robbin, Transversal mappings and flows, W. A. Benjamin, Inc., New York-Amsterdam, 1967. An appendix by Al Kelley. MR 0240836
  • James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
    • A. Gottlieb, Thesis, Brandeis University, Waltham, Mass., 1973. C. Robinson (unpublished).
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 53 (1975), 167-171
  • MSC: Primary 58C20; Secondary 34A25
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0385915-0
  • MathSciNet review: 0385915